Pappas–Rapoport flatness conjecture for spin local models at parahoric level

Let $F/F_0$ be a quadratic extension, let $(V,\phi)$ be a symmetric space of dimension $2n+2$, and let $I\subset [0,n]$ be non-empty. Let $\RM^\pm_I$ be the spin local model over $\CO_F$, and let $\RM^{\pm\loc}_I$ be the schematic closure of its generic fiber in $\RM^\pm_I$. Pappas–Rapoport's flatness conjecture. The spin local model $\RM^\pm_I$ is flat over $\CO_F$. Equivalently, $\RM^\pm_I=\RM^{\pm\loc}_I$. The paper states that the schematic closure is identified with a Pappas–Zhu local model and has strong geometric properties, but the supplied parser status does not establish that the conjecture itself is resolved.